The absolute value of the difference of two numbers is the distance between those two numbers on the number line. For example, \left\lvert a - b\right\rvert∣a−b∣open vertical bar, a, minus, b, close vertical bar is the distance between aaa and bbb. Remember that distance (and absolute value!) is never negative. Hint #22 / 4
Since aaa is negative and the other expressions use absolute value (i. e. distance), aaa is the expression with the least value.
Hint #33 / 4
\left\lvert b - c \right\rvert < \left\lvert a - b\right\rvert∣b−c∣<∣a−b∣open vertical bar, b, minus, c, close vertical bar, is less than, open vertical bar, a, minus, b, close vertical bar because the distance between bbb and ccc is less than the distance between aaa and bbb.
\left\lvert a - b \right\rvert < \left\lvert a - c \right\rvert∣a−b∣<∣a−c∣open vertical bar, a, minus, b, close vertical bar, is less than, open vertical bar, a, minus, c, close vertical bar because the distance between aaa and bbb is less than the distance between aaa and ccc.
Hint #44 / 4
The expressions are ordered from least to greatest below:
aaa \left\lvert b - c\right\rvert∣b−c∣open vertical bar, b, minus, c, close vertical bar \left\lvert a - b\right\rvert∣a−b∣open vertical bar, a, minus, b, close vertical bar \left\lvert a - c\right\rvert∣a−c∣open vertical bar, a, minus, c, close vertical bar
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